Question: Simplify the following expression: $ q = \dfrac{7}{r - 4} + \dfrac{-5}{4} $
Explanation: In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{4}{4}$ $ \dfrac{7}{r - 4} \times \dfrac{4}{4} = \dfrac{28}{4r - 16} $ Multiply the second expression by $\dfrac{r - 4}{r - 4}$ $ \dfrac{-5}{4} \times \dfrac{r - 4}{r - 4} = \dfrac{-5r + 20}{4r - 16} $ Therefore $ q = \dfrac{28}{4r - 16} + \dfrac{-5r + 20}{4r - 16} $ Now the expressions have the same denominator we can simply add the numerators: $q = \dfrac{28 - 5r + 20}{4r - 16} $ $q = \dfrac{-5r + 48}{4r - 16}$